A quick trip home and tb46 has this done for me. Thank you. So tapped horns are like others in that a high q driver is not suited. OK, that's why I have to semi-plug [aperiodic] the port even in an oversized repurposed box. If you look at the pictures in the link you can see why the sensitivity is so low on that woofer. Not a lot of coil sitting in the gap.

Here's the easiest way to visualize how the isobaric tapped horn will provide more output:

We know that the box size of a VAS config can be halved. But another option is to use the same size box, with four woofers.

In that configuration, we'll have the following advantages over the same box with one woofer:

1) Due to the fact that we have four voice coils, the amount of power going into each coil will be reduced by 75%. YES it is true that our efficiency rating is exactly the same for a four woofer isobaric versus a single woofer setup. And that may seem like a criminal waste of money. But a 75% reduction in voice coil power is significant.

2) Due to the fact that we have twice the cone area, excursion is halved for the same SPL level.

Combine those two things together, a reduction in displacement AND a reduction in voice coil heat, and you have a recipe for a MONSTER of a tapped horn.

Or, better yet, split the horn in half. Instead of using two isobaric pairs in one cabinet, use one isobaric pair in the cabinet, and put the other sub somewhere else in the room. You'll still enjoy all the advantages of isobaric, and you'll also get the benefits of the Geddes multi sub approach.

You can model all of this in hornresp by the way; just take a design, copy it to a new page, and substitute two series-wired isobaric woofers wired in parallel for the single woofer of the original design.

Let's start with a real world example, ok?

This is XOC1's TH, as documented on this forum

Here's the output of the XOC1 sub, with 1000 watts into 4ohms and a B&C 15TBX100 woofer. But we can't hit that SPL, because we're displacement limited.

So in my next post, I'll show you how to address that using isobaric woofers...

The graph above pits four of the Alpine Type S 10" woofer against one of the B&C 15TBX100s. The enclosure is identical; it's XOC1's box.

In the graph, we see that performance is similar; the response shape is mostly dictated by the horn, not the driver. Four of the Alpines cost about $50 more than one of the B&Cs. But the Alpines have 50% more displacement, and four of the Alpines have 70% more voice coil area than the B&C.

The first uses four of the Alpine tens.
The second uses SIXTEEN of the Alpine tens, but in isobaric pairs. (Box size is exactly the same.)

Here's the frequency response.
Yes, it's exactly the same.

Here's the impedance curve. Same here too.

Ah, here's the money shot!
The isobaric box has half the excursion. And since subs are generally limited by displacement, that means the isobaric box will get louder than the conventional box, as long as you have enough power to get there.

The icing on the cake is you have four times as many voice coils. So thermal modulation and thermal compression will be dramatically reduced.

Of course, this box is completely unnecessary if you don't have a big amp to drive it
The Behringer Europower amp would be awesome on this. 4000 watts into this box works out to 250 watts per voice coil, which is well within the Alpine's limits. Heck, you could probably halve the box size, use half the woofers, and dump 500 watts into each one. Eight of the Alpine tens and one of the Behringer amps would cost about $1100. (Amazon and Wal Mart have the amp for $275, and the Alpine woofer is readily available for $100 at various retailers.)

Now, obviously it's going to be a bit tricky to squeeze sixteen tens into this enclosure :P

A couple of options:

You could mount the drivers like the Tymphany LAT

or...

You could double the length of S4-S5

Obviously, the tens are 'home theater friendly' because you could take XOC1's box and halve the width. So instead of being 21" wide it would be 11.5" wide.

Isobaric loading does not cut excursion in half. You are coupling the drivers together and utilizing only the effective SD and therefore displacement of a single driver. The positive cycle from one and the negative from the other. You actually need twice the driver displacement for the same output of a single conventional mounted driver.

If you are utilizing the displacement and SD of all of the drives then it is not an isobaric alignment. That would be just loading more drivers into the system.

Here's an example:
1: one woofer in a 56L box, with an efficiency of 90db and a maximum SPL of 110db
2: the same woofer in an isobaric pair. Efficiency has dropped to 87db, but max SPL is the same. (This assumes that maximum output is limited by xmax)
3: add another cab, for a total of two isobaric pairs, and your maximum output will be 6dB higher than a single woofer.

Patrick's right. For the same enclosure volume, at the same excursion per driver, you get twice the displacement, 6dB more output.

A single driver might need a 50 litre enclosure and displace 0.2 litres of air at xmax.
Two drivers in isobaric only need a 25 litre enclosure but still only displace 0.2 litres at xmax. Same output.
You can either build another 25 litre enclosure for a second isobaric pair, or put two pairs in the original 50 litre enclosure. Either way, you now get 0.4 litres of displacement at xmax. 6 dB more output out of the same enclosure volume needed for a single driver.

Patrick,
One slight problem with isobaric driver setups is that they aren't perfect. The models assume that the two cones are rigidly coupled, whereas there is actually a compliance between them. Exporting the above Hornresp simulations to AkAbak and allowing a volume between the cones shows that the driver excursions become quite mismatched at some frequencies. Instead of the expected 6 dB increase in output for 4x the drivers at xmax, you only get about 5 dB because the mouth-side drivers reach xmax before the throat-side drivers.

The diameter of the driver's mouth is 230 mm, and the mouth opening is 24 mm deep. That's about a litre. Add about another half litre for the volume of the cone. Double this because the drivers are face to face. Putting that between the drivers in AkAbak gives the attached excursion for the two drivers. The black trace is the "inside" driver nearest the throat.

Still, 5 dB more in the same size enclosure is a lot better than nothing.

Incidentally, instead of modelling the horn with 4x and 16x drivers, I divided the horn areas by 4 and used 1 driver and 4 drivers.